Microelectromechanical system (MEMS) capacitive electrostatic comb-drive, closed-loop, in-plane, micromachined, capacitive pick-off accelerometer devices, closed-loop Coriolis rate gyroscope devices, and closed-loop capacitive pressure and force measuring devices are generally well-known. In particular, silicon-based, micromachined accelerometers are displacing accelerometers of more mature architectures in current applications, and are creating new markets where the advantages of small size and low cost are enabling qualities. One critical area of performance that poses a major challenge for MEMS capacitive accelerometers is vibration rectification. Vibration rectification is the change in the time-average accelerometer output due to input vibration. Vibration rectification manifests as an apparent change in the DC acceleration when none is being experienced.
Current MEMS capacitive accelerometers, Coriolis rate gyroscope devices, and closed-loop capacitive force measuring devices have very poor vibration rectification performance. For example, an input vibration of 10 Grms along the input axis of a known electrostatic comb-drive MEMS capacitive pick-off accelerometer is able to change the average output by as much as 0.1 g's. This large vibration rectification makes these accelerometers unsuitable for current tactical and navigation-grade applications.
In a closed-loop capacitive pick-off accelerometer, rectification error is driven by several sources. For example, rebalance force is not linear relative to the voltage applied to the electrostatic comb-drive. The rebalancing force is proportional to the square of the applied voltage difference between sets of interacting moveable and fixed comb teeth. There are several well-known ways to accomplish linearization of the applied voltage. For example, a square root function can be placed in the feedback loop. The various methods of linearizing this relationship, however, are not relevant to the present invention.
Scale factor may have asymmetry in a closed-loop capacitive pick-off accelerometer. That is, the scale factor in the positive input direction may not equal the scale factor in the negative direction. The scale factors in the two directions must match to avoid rectification. This is also well-known, can be corrected for, but is not relevant to the present invention.
A third source of rectification in a closed-loop capacitive pick-off accelerometer is a dependence of rebalance force on proof mass position. In current art, closed-loop MEMS capacitive pick-off accelerometers with electrostatic feedback use one of two configuration options.
FIG. 1 illustrates a parallel-plate drive configuration which is widely utilized in the prior art. A closed-loop capacitive pick-off accelerometer 1 of the prior art utilizes a series of parallel plate pairs 3. In each pair 3, one tooth 5 is fixed relative to a supporting frame 7, and the other tooth 9 is movable and part of a movably suspended proof mass 11. With in-plane proof mass motion, a gap 13 between the two plates 5, 9 vanes, as indicated by the arrow. For a given voltage differential across the two plates 5, 9, the force is proportional to 1/gap2, and so is highly nonlinear with the proof mass motion that results from vibration. Because of this relationship, for a constant applied voltage, vibration raises the time-average force and a rectification error results. This parallel plate drive configuration provides a large nominal force, but very poor rectification performance.
FIG. 2 illustrates a lateral comb drive configuration which is also known in the prior art. The lateral comb drive concept is taken from non-accelerometer applications where a constant force is desired that is independent of the comb engagement or overlap. In a lateral comb drive device 15, a “constant” force drive is achieved by making both the overlap 17 of the fixed and movable comb teeth 19, 21 and the end-gap 23, 25 between the movable teeth 19 and the fixed frame 27 and between the fixed teeth 21 and the movable proof mass 29, large relative to both the tooth side spacing 31 and the allowed relative lateral motion 33. In applications where space is not at a premium, and only a low-g operating range is required, the lateral comb drive maybe an acceptable solution to the vibration rectification problem in MEMS closed-loop accelerometers. However, lateral drives of this type consume a large amount of space, add mass, and do not provide a large nominal force. Therefore, if low rectification is desired, force must be sacrificed. These lateral comb drives also result in a relatively large nominal capacitance between the sets of fixed and movable comb teeth 19, 21, which is potentially undesirable from an electronics viewpoint. For these reasons, this method is rarely used.
A fourth source of rectification is a force that a damping fluid exerts on the proof mass during vibration. Typically, MEMS accelerometers rely on gas damping to achieve acceptable dynamic performance. Gas-spring damping effects, however, often produce a non-zero time average force on the proof mass as it travels through a cycle of vibration. Many variables affect this rectification error which is a function of the detailed geometry of the damping gaps, the gas type, pressure and temperature, and the magnitude and frequency of the input vibration. The result is a highly complex fluid dynamics problem. Furthermore, the magnitude of this rectification error is potentially extremely large.
Therefore, devices and methods for overcoming these and other limitations of typical state of the art MEMS accelerometers are desirable.